Branching Processes
Branching Processes

Author: Asmussen

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 468

ISBN-13: 1461581559

DOWNLOAD EBOOK

Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.

Branching Processes
Branching Processes

Author: Krishna B. Athreya

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 301

ISBN-13: 3642653715

DOWNLOAD EBOOK

The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.

Workshop on Branching Processes and Their Applications
Workshop on Branching Processes and Their Applications

Author: Miguel González

Publisher: Springer Science & Business Media

Published: 2010-03-02

Total Pages: 304

ISBN-13: 3642111564

DOWNLOAD EBOOK

One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.

The Theory of Branching Processes
The Theory of Branching Processes

Author: Theodore Edward Harris

Publisher: Springer

Published: 2012-05-29

Total Pages: 232

ISBN-13: 9783642518683

DOWNLOAD EBOOK

It was about ninety years ago that GALTON and WATSON, in treating the problem of the extinction of family names, showed how probability theory could be applied to study the effects of chance on the development of families or populations. They formulated a mathematical model, which was neglected for many years after their original work, but was studied again in isolated papers in the twenties and thirties of this century. During the past fifteen or twenty years, the model and its general izations have been treated extensively, for their mathematical interest and as a theoretical basis for studies of populations of such objects as genes, neutrons, or cosmic rays. The generalizations of the GaIton Wa,tson model to be studied in this book can appropriately be called branching processes; the term has become common since its use in a more restricted sense in a paper by KOLMOGOROV and DMITRIEV in 1947 (see Chapter II). We may think of a branching process as a mathematical representation of the development of a population whose members reproduce and die, subject to laws of chance. The objects may be of different types, depending on their age, energy, position, or other factors. However, they must not interfere with one another. This assump tion, which unifies the mathematical theory, seems justified for some populations of physical particles such as neutrons or cosmic rays, but only under very restricted circumstances for biological populations.

Branching Processes in Biology
Branching Processes in Biology

Author: Marek Kimmel

Publisher: Springer Science & Business Media

Published: 2006-05-26

Total Pages: 242

ISBN-13: 0387216391

DOWNLOAD EBOOK

This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.

Branching Processes
Branching Processes

Author: Patsy Haccou

Publisher: Cambridge University Press

Published: 2005-05-19

Total Pages: 342

ISBN-13: 9780521832205

DOWNLOAD EBOOK

This book covers the mathematical idea of branching processes, and tailors it for a biological audience.

Classical and Modern Branching Processes
Classical and Modern Branching Processes

Author: Krishna B. Athreya

Publisher: Springer

Published: 1997

Total Pages: 368

ISBN-13:

DOWNLOAD EBOOK

This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13-171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes.

Measure-Valued Branching Markov Processes
Measure-Valued Branching Markov Processes

Author: Zenghu Li

Publisher: Springer Science & Business Media

Published: 2010-11-10

Total Pages: 356

ISBN-13: 3642150047

DOWNLOAD EBOOK

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups. The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Spatial Branching Processes, Random Snakes and Partial Differential Equations
Spatial Branching Processes, Random Snakes and Partial Differential Equations

Author: Jean-Francois Le Gall

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 170

ISBN-13: 3034886837

DOWNLOAD EBOOK

This book introduces several remarkable new probabilistic objects that combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial differential equations (PDE). The Brownian snake approach is used to give a powerful representation of superprocesses and also to investigate connections between superprocesses and PDEs. These are notable because almost every important probabilistic question corresponds to a significant analytic problem.

Branching Processes and Their Applications
Branching Processes and Their Applications

Author: Inés M. del Puerto

Publisher: Springer

Published: 2016-09-06

Total Pages: 331

ISBN-13: 3319316419

DOWNLOAD EBOOK

This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.